Parametric primitives through python script
I don't know if you're still searching for this but I found something that may be what you're looking for. It's an Add-On called "Wonder Mesh". The Add-On allows you to generate and edit the parameters of its available primitives. That being said, the author states that you need to convert the object to a "regular mesh" if you want to modify the primitive. It overwrites modifications to the Object Data that were made in Edit Mode.

Here is a direct link to the Add-On:

https://blendermarket.com/products/wonder-mesh

(You can purchase it here or go to the bottom of the page for the GitHub link)

Here is a video on the most recent version for Blender v2.8:

https://www.youtube.com/watch?v=zUFWcGAoDPw

Here is a video on a older version (in case it's useful): 

https://www.youtube.com/watch?v=WCnwnwuDbfk